System and method for generating dithering sequences with minimum value for seismic exploration

ABSTRACT

System and method for shooting plural seismic sources Si in a marine acquisition system with a deblending-designed dithering sequence DS new . The method includes generating the deblending-designed dithering sequence DS new  to include random dithering times D i , a range of the dithering times D i  being larger than a preset, non-zero, minimum value pmv; selecting a shooting sequence SS for the plural seismic sources Si; and shooting the plural seismic sources Si with the deblending-designed dithering sequence DS new , based on the shooting sequence SS. All odd or all even members of the shooting sequence SS are shot with zero dithering times.

BACKGROUND Technical Field

Embodiments of the subject matter disclosed herein generally relate tomethods and systems related to seismic exploration and, moreparticularly, to mechanisms and techniques for generating ditheringsequences, having a minimum dithering value, to be applied to seismicsources for generating seismic waves.

Discussion of the Background

Marine seismic data acquisition and processing generate a profile(image) of a geophysical structure under the seafloor. While thisprofile does not provide an accurate location of oil and gas reservoirs,it suggests, to those trained in the field, the presence or absence ofthese reservoirs. Thus, providing a high-resolution image of thestructures under the seafloor is an ongoing process and the goal for anyseismic acquisition survey.

During a seismic gathering process, as illustrated in FIG. 1, a seismicacquisition system 100 includes a vessel 102 that tows a seismic spread104 (i.e., plural streamers 106 and associated equipment, e.g., float108). The streamers may be disposed horizontally, i.e., lying at aconstant depth relative to a surface of the ocean, slanted or curvedrelated to the ocean surface. Each streamer 106 includes plural seismicsensors 110 (only two are illustrated for simplicity) for recordingseismic data.

The vessel also tows two seismic source arrays 122 and 124 that areconfigured to generate seismic waves. Each seismic source arraytraditionally includes three sub-array 122A-C and each sub-arrayincludes a given number of seismic source elements. A seismic sourcesub-array 122A is illustrated in FIG. 2 having a float 130 to whichseven seismic source elements 132 to 144 are attached. The typicalseismic source element is an airgun.

The seismic waves generated by the seismic source arrays propagatedownward, toward the seafloor, and penetrate the seafloor (subsurface)until, eventually, a reflecting structure reflects the seismic wave. Thereflected seismic wave propagates upward until it is detected by theseismic sensors on the streamers. Based on this data, an image of thesubsurface is generated.

Marine seismic acquisition employing more than two sources is nowregularly being used due to the prospect of denser sampling,particularly in the crossline direction, at a similar cost as aconventional acquisition. Due to a reduced temporal shot spacing, finaldata quality depends on the capability of the processing phase toseparate (deblend) the overlapping energy from different sources.

The use of simultaneous shooting has increased in recent years due toits ability to increase efficiency, fold and/or spatial data sampling,often at little or no extra cost (Poole et al., 2014; Peng et al.,2013). In marine acquisition, a commonly used approach to improvecrossline sampling is to increase the number of sources beyond theconventional dual-source acquisition (Hager et al., 2016). FIGS. 3A-3Cillustrate this idea by comparing the cross-line sampling of aconventional survey having two sources S1 and S2 (see FIG. 3A), atriple-source S1 to S3 arrangement (see FIG. 3B) and a hexa-source (S1to S6) acquisition system (see FIG. 3C). Each system has the same numberof receivers R (the figures show the streamer positions and eachstreamer has plural receivers). As can be seen at the bottom of thesefigures, the extra sources effectively improve the cross-line sampling(the density of the wave reflections at the bottom of the figures isincreased. The X axis of the figures represent the cross-line and the Yaxis is the depth.

To maintain the inline fold, it is tempting to decrease the shot-pointinterval as the number of sources increases. This will lead tooverlapping waves generated by the sources that need to be separatedduring the processing stage in a process commonly referred to as“deblending.” To allow for effective deblending, it is common practiceto apply a small random dither to the firing times of each individualsource (individual sources are illustrated in FIG. 2). The basic conceptis explained with reference to FIGS. 4A and 4B. FIG. 4A shows fourconsecutive shot gathers SG1 to SG4 from one source-cable combination(i.e., a single cable), where the source was placed directly over thestreamer spread (see, for example, Vinje et al., 2017). In FIG. 4A,horizontal lines 400 to 406 indicate how the dithered firing times ofeach source vary from shot to shot (line 400 corresponds to the firstshot, line 402 corresponds to the second shot, line 404 corresponds tothe third shot and line 406 corresponds to the fourth shot). When suchdithered data is sorted to, for example, in the common channel domain(i.e., a single channel from a single streamer is selected and all theseismic data recorded by this channel over time is plotted—and thefiring times are aligned), as illustrated in FIG. 4B, the first shot 410appears as straight lines 412 while the next (interfering) shots 414appear as ‘random’ noise. Note that the dither shown in FIG. 4A is justrandom, with no other attributes. In other words, a software routine isused to generate random numbers in a given interval and these randomnumbers are applied as dither to the pre-determined shot times of theindividual sources.

Most deblending algorithms generally take advantage of the dither bytrying to suppress the blending noise and enhance the coherent signal.Examples of both passive and active early deblending algorithms can befound in Babier and Staron, 1971, Vaage et al., 2002, Moore et al., 2008and Maraschini et al. 2012. It is noted that in the last decade(2007-2017), at least 200 publications on deblending can be found in theEAGE and SEG archives.

However, the existing deblending algorithms are normally not capable ofperfect deblending. One reason for this failure of the existing methodsis believed to be the clustering of the random dithering times that areapplied to the shooting times of the individual sources. Another reasonfor this failure of the existing methods is that the clean record lengthof the recorded traces is not long enough in certain situations.

Thus, it is desired to produce new more optimal dithering sequences thatovercome these problems.

SUMMARY

According to an embodiment, there is a method for shooting pluralseismic sources Si in a marine acquisition system with adeblending-designed dithering sequence DS_(new). The method includesgenerating the deblending-designed dithering sequence DS_(new) toinclude random dithering times D_(i), a range of the dithering timesD_(i) being larger than a preset, non-zero, minimum value pmv, selectinga shooting sequence SS for the plural seismic sources Si; and shootingthe plural seismic sources Si with the deblending-designed ditheringsequence DS_(new), based on the shooting sequence SS. All odd or alleven members of the shooting sequence SS are shot with zero ditheringtimes.

According to another embodiment, there is a method for shooting pluralseismic sources Si in a marine acquisition system with adeblending-designed dithering sequence DS_(new). The method includesgenerating the deblending-designed dithering sequence DS_(new) toinclude random dithering times D_(i), wherein either all odd or all evendithering times Di of the deblending-designed dithering sequenceDS_(new) are null, and the other of the all odd or all even ditheringtimes have a range that is larger than a preset, non-zero, minimum valuepmv, and shooting the plural seismic sources Si with thedeblending-designed dithering sequence DS_(new).

According to yet another embodiment, there is a computing device fordriving plural seismic sources Si in a marine acquisition system with adeblending-designed dithering sequence DS_(new). The computing deviceincludes a processor configured to generate the deblending-designeddithering sequence DS_(new) to include random dithering times D_(i), arange of the dithering times D_(i) being larger than a preset, non-zerominimum value pmv, and select a shooting sequence SS for the pluralseismic sources Si. The computing device also includes an interfaceconnected to the processor and configured to send instructions to shootthe plural seismic sources Si with the deblending-designed ditheringsequence DS_(new), based on the shooting sequence SS. All odd or alleven members of the shooting sequence SS are shot with zero ditheringtimes.

According to still another embodiment, there is a non-transitorycomputer readable medium including computer executable instructions,wherein the instructions, when executed by a processor, implementinstructions for generating a deblending-designed dithering sequencesDS_(new) for marine seismic sources S_(i) in a marine acquisitionsystem, as noted above.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 is a schematic diagram of a conventional seismic survey system;

FIG. 2 is a side view of a sub-array of an array source;

FIGS. 3A-3C illustrate CMP-bins for a two source setup, a triple-sourcesetup and a hexa-source setup;

FIG. 4A illustrates consecutive seismic shot gathers and FIG. 4B theseismic data sorted in a common channel;

FIG. 5A illustrates a marine seismic acquisition system, FIG. 5Billustrates a random dithering sequence; and FIG. 5C illustrates a noveldithering sequence;

FIGS. 6A and 6B are flowcharts of two methods for generating a ditheringsequence in which the odd or even members are zero and all the othermembers are larger than a minimum preset value;

FIG. 7 illustrates a method for generating a random low-discrepancysequence;

FIG. 8A illustrates a seismic acquisition system having three sourcesand FIG. 8B illustrates the dithers of two sources when the data isaligned with a third source;

FIGS. 9A and 9B illustrate two uniform random distributions, and FIGS.9C and 9D illustrate a result of the combination of the two uniformrandom distributions;

FIG. 10A illustrates a basic algorithm for calculating ditheringsequences for three different sources so that a combination of any twoof the dithering sequences results in a uniform random low-discrepancysequence and FIG. 10B illustrates the same algorithm as a pseudo-code;

FIGS. 11A and 11B illustrate three such dithering sequences for threedifferent sources and FIGS. 12A and 12B show the combinations of pairsof such dithering sequences that resulted in uniform randomlow-discrepancy sequences;

FIGS. 13A and 13B illustrate N+1 and N+2 effective dithers for a typicalrealization;

FIGS. 14A and 14B are flowcharts of a method for generating ditheringsequences that, when combined, result in a uniform randomlow-discrepancy sequence;

FIG. 15A illustrates a synthetic reflector, FIG. 15B illustrates anIrwin-Hall dither and FIG. 15C illustrates a uniform randomlow-discrepancy dither;

FIG. 16 illustrates various results obtained with the Irwin-Hall ditherof FIG. 15B and the uniform random low-discrepancy dither of FIG. 150;and

FIG. 17 illustrates a computing device in which the methods discussedherein may be implemented.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims. The following embodimentsare discussed, for simplicity, with regard to two and three seismicsources that are shot according to dithering sequences that have specialproperties. However, the embodiments to be discussed next are notlimited to two or three seismic sources, but they may be applied to ahigher number of sources.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with an embodiment is included in at least oneembodiment of the subject matter disclosed. Thus, the appearance of thephrases “in one embodiment” or “in an embodiment” in various placesthroughout the specification is not necessarily referring to the sameembodiment. Further, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

According to an embodiment, a source dithering sequence to be applied toplural source arrays is generated. The generated source ditheringsequence guarantees a clean record length for the recorded data, to beused by various deblending algorithms. According to this embodiment, themethod applies a zero dithering time to each odd or even source of ashooting sequence, and a random dithering time, having a minimum range,to the other members in the sequence. Each random dithering time fallsinto the range, which is selected to have a value larger than a minimum,non-zero, value. The random dithers can be generated in various ways,for example, with methods to be discussed herein in more detail, with arandom generator, etc.

In this regard, FIG. 5A shows a marine seismic acquisition system 500that includes a vessel 502 that tows three source arrays 504 (S1), 506(S2), and 508 (S3) along a sail line 510 (which coincides with theinline direction X). Note that the number of source arrays can be largeror smaller. Each source array Si includes plural source elements, whichmay grouped in sub-arrays. For example, FIG. 5A schematicallyillustrates that each source array has two sub-arrays. A source elementmay be an air gun or a vibrational element. The three source arrays areoffset by a given distance along the cross-line direction Y.

One possible shooting sequence SS for the sources S1 to S3 isillustrated in FIG. 5B. In this embodiment, the positions SP_(i) atwhich the sources are supposed to be shot, with no dithering times, arecalculated first. Then, a dither sequence DS is calculated, whichinclude plural dithering times Di, one for each source. Note that theplural dithering times D_(i) may be randomly generated, but they fallinto a given range (dashed box in FIG. 5B). In one application, therange is centered on the time to which the source is expected to be shotat its given shot point SP_(i) if the source would be fired with nodithering times. However, because the sources are fired with a ditheringtime D_(i), the first source S1 is actually shot at a first shootingpoint P₁, which is different than SP₁ for a dithering time D₁, thesecond source S2 is actually shot at a second shooting point P₂, whichis different than SP for a dithering time D₂, and the ith source Si isactually shot at an ith shooting point P_(i), which is different thanSP_(i) for a dithering time D_(i). A distance between two shootingpositions SP₁ and SP₂ is given by a shot point interval SPI, which isconstant while the sources are advancing along the sail line 510.

FIG. 5B shows that an absolute value of each dithering time D_(i) has amaximum time range given by max|δt|. For this scenario, the guaranteedclean record length (i.e., that portion of the trace for which a signalfrom a previous shooting is not mixed with a signal from the currentshooting) is given by RL_(clean)=SPI/BSP−2 max(δt), where BSP is thebottom speed of the vessel towing the sources. However, when there is anincrease in the speed of the vessel, for example, because of a tailcurrent, the time between consecutive shots decreases, which results ina shorter clean record time, which is not desirable. U.S. PatentApplication Publication No. 2018/052248 proposes to adaptively decreasethe dithering time to ensure a minimum clean record time. The problemwith this approach is that a reduction in the dithering timeautomatically decreases the ability to attenuate (i.e., deblend) thefollowing shot.

Therefore, according to the embodiment illustrated in FIG. 5C, it isproposed to further constrain a range of the dithering times in asequence, by imposing a preset minimum dithering value on the range ofthe dithering sequence to ensure proper deblending of the collectedseismic data. This preset minimum dithering value is derived based onthe needs for processing the seismic data, which depends on the recordedfrequencies, the bin, etc. In typical settings, the minimum alloweddithering value can be in the range of 200-1,000 ms, but other valuesmay also be used.

As illustrated in FIG. 5C, for a vessel that tows three source arrays S1to S3, a shooting sequence SS_(new) includes firing the first source S1first, followed by shooting the second source S2, then the third sourceS3, again the first source S1, and so on. However, the shooting sequenceSS_(new) may include other combinations, i.e., firing first the firstsource, then the second source, then again the first source, then thethird source, and so on. Other combinations of the three sources may beused. In one application, the number of sources may be larger ofsmaller.

Assuming that the shooting sequence SS_(new) is as indicated in FIG. 5C,the first source S1 is shot with no dithering time D₁ (or a zerodithering time), the second source S2 is shot with a random ditheringtime D₂, the third source S3 is shot with no dithering time D₃ (or azero dithering time), the first source S1 is shot with a randomdithering time D_(i), and so on. In other words, the deblending-designeddithering sequence DS_(new) used in this embodiment together with theshooting sequence achieve the following result: each odd member of theshooting sequence is shot with no (or zero) dithering time and eachother member of the shooting sequence is shot with a random ditheringtime. Each random dithering time has an absolute value smaller than themaximum value, max|δt|. This maximum value is illustrated in FIGS. 5Band 5C and it is associated with half of a value of the range of thedithering sequence. In addition, according to this embodiment, eachrandom dithering time falls into the range of the dithering sequence andthe range has a minimum value, that is larger than a preset minimumvalue (pmv). For illustration, if the dithering times of a sequence havevalues between −1 and 1, the range of this sequence is 2. In oneapplication, the preset minimum value is selected to be 200 ms. Inanother application, the present minimum value is selected to be 500 ms.Any value between these two specific values may be used as the presetminimum value for the range of the dithering sequence. Depending on thesurvey, other values for the pmv may be selected. The preset minimumvalue pmv, as discussed above, is determined for each seismic surveybased on the objective of the survey, the characteristics of thesubsurface, the recorded frequency, the bin, and the need to deblend thevery low frequency content of the seismic signal. This means that thelower the frequency, the larger the range of dithering times needed tobe able to deblend the signal.

With this novel dithering sequence, the guaranteed clean record lengthis given by RL_(clean)=SPI/BSP−max(δt), which is larger than for thecase discussed above with regard to FIG. 5B. Thus, the present ditheringsequence is not only appropriate for deblending operations, but it alsoensures that proper deblending can be performed on the recorded seismicdata.

Further, the preset minimum value pmv can be adaptively increased if thevessel slows down. This may allow the process to improve the deblendingof the overlapping shots, while still maintaining a minimum clean recordtime. If the novel dithering sequence is to be implemented on the vessel502, in a controller, which is discussed later, the controller wouldfollow the following steps (see either FIG. 6A or FIG. 6B for aflowchart of a method to shot seismic sources based on the noveldithering sequence). The method illustrated in FIG. 6A starts with astep 600 of generating a deblending-designed dithering sequence DS_(new)that includes random dithering times D_(i). A range of the ditheringtimes is larger than the preset, non-zero, minimum value pmv. In step602, a shooting sequence SS for the plural seismic sources Si isselected. In step 604, the plural seismic sources Si are shot with thedeblending-designed dithering sequence DS_(new), based on the shootingsequence SS. All odd or all even members of the shooting sequence SS areshot with zero dithering times, as illustrated in FIG. 5C. This meansthat either the deblending-designed dithering sequence DS_(new) hasevery other member zero, or the deblending-designed dithering sequenceDS_(new) is applied only to the other member of the shooting sequence.

In another embodiment, illustrated in FIG. 6B, the method starts with astep 610 of generating the deblending-designed dithering sequenceDS_(new) to include random dithering times D_(i), where either all oddor all even dithering times Di of the deblending-designed ditheringsequence DS_(new) are null and a range for the other of the all odd orall even has a value larger than a preset, non-zero, minimum value pmv,and a step 612 of shooting the plural seismic sources Si with thedeblending-designed dithering sequence DS_(new).

The deblending-designed dithering sequence can be randomly generated orbased on any other known method. A novel method to generate thedithering sequence is discussed later. The method of generating thedithering sequence in step 600 or step 610 may be configured to have amaximum value built in and thus, it generates the dithering sequence sothat the range is smaller than the maximum value. The same method may beimplemented with dithering spaces instead of dithering times, where thedithering spaces are random distances with which the sources aredisplaced relative to their regular shooting points, before shooting thesources.

According to an embodiment, constructing a new dithering sequence is nowdiscussed. Source dithering is designed in order to help the deblendingprocess. In particular, it will be discussed how to construct ditheringsequences for the various sources involved in a seismic survey so that,when combining pairs of such sequences, the resulting sequence may be adiscrete, uniform random, low-discrepancy sequence. In probabilitytheory and statistics, a discrete uniform distribution is a symmetricprobability distribution where a finite number of values are equallylikely to be observed; every one of n values has equal probability 1/n.Another way of saying “discrete uniform distribution” would be “a known,finite number of outcomes equally likely to happen.” As plural sourcesare fired simultaneously (this term is understood to mean that thesources are fired with a small time delay, the “dither,” of “jitter”relative to each other), parts of the waves generated by source “n” areblended with parts of the waves generated by source “m” when recorded bya given seismic receiver. As previously discussed with regard to FIGS.4A and 4B, when the recordings are time aligned for a given source “n,”in the common channel domain, the dithering for the given source “n” isleaking into the dithering of the other sources, e.g., source “m.” Thismeans that although the dithering of the given source was uniform randomand the dithering of the other sources were also uniform random, thecombined (leaked) dither will have a distribution, which is not idealfor the deblending processes. A well-known fact in the field ofstatistics is that the sum of two uniform random dithering sequencesforms a so called Irwin-Hall sequence, which is not uniform random. Thisproblem of the existing acquisition methods is now discussed in moredetail and solutions are proposed that prevent the leaked dithering fromclustering.

As already discussed above, it is common to generate uniformly randomdithering values and apply them to the sources being shot in a givenseismic survey. The random dithering ensures that the blending noise isfairly uniformly spread out within a certain selected time-range. Byanalyzing these random dithering values, it is found that a clusteringof some data points is present. A pure random sequence will have somerandom clustering, i.e., some nearby values that sometimes tend to bevery close, while others seem to be far apart.

For deblending purposes, the clustering is undesired because thecollected data may become more coherent, and consequently more difficultto separate in the deblending process. A better and novel solutionproposed in this embodiment is using a so called “low-discrepancy”random sequence, which works to avoid this random clustering. The“discrepancy” of a sequence is defined in mathematics as follows. Asequence {s₁, s₂, s₃, . . . } of real numbers is said to be uniformlydistributed, if the proportion of terms of the sequence falling in asubinterval is proportional to the length of that sub-interval. In otherwords, if the sequence includes 9 terms s₁ to s₉, and the subinterval isa length of 1 m along an axis, the sequence is uniformly distributed ifthere is a distance of 10 cm between any adjacent two terms along agiven axis. If the space in which the sequence is defined is differentfrom an axis (e.g., the space has a volume), then a “measure” isintroduced on that space and the “length” of the interval is replaced inthe above definition by the “measure” of that space.

This can be expressed in mathematics terms as:

$\begin{matrix}{{{\lim\limits_{n->\infty}\frac{{\left\{ {s_{1},\ldots\mspace{14mu},s_{n}} \right\}\bigcap\left\lbrack {c,d} \right\rbrack}}{n}} = \frac{d - c}{b - a}},} & (1)\end{matrix}$where the numerator of the first term denotes the number n of elementsfrom the sequence that are between numbers c and d, which define thesubinterval. Numbers a and b define an interval in which all theelements of the sequence are distributed.

The discrepancy D_(N) for the sequence {s₁, s₂, s₃, . . . } with respectto the interval [a, b] is defined as:

$\begin{matrix}{D_{N} = {\sup\limits_{a \leq c \leq d \leq b}{{{\frac{\left\{ {s_{c},\ldots\mspace{14mu},s_{N}} \right\} }{N} - \frac{d - c}{b - a}}}.}}} & (2)\end{matrix}$

A sequence is uniformly distributed if the discrepancy D_(N) tends tozero as N tends to infinity. Thus, in the following, the discrepancy ofa sequence is low if the proportion of points in the sequence fallinginto an arbitrary set B is close to proportional to the measure of B, aswould happen on average (but not for particular samples) in the case ofan uniformly distributed sequence. More mathematical details about thistopic may be found in Braaten and Weller, 1979 and Kocis and Whiten,1997 and the references within.

Some well-known low-discrepancy sequences are the Halton, Sobol, andFaure sequences. However, in their basic form, these sequences are notnecessarily ideal for use in a seismic acquisition setting. A few commonproblems of these sequences are that the derivative and sum of thesesequences may not be random, or that a given sequence may be relativelyshort.

In Borselen and Baardman, 2014, an elaborate algorithm was introducedthat made sure that consecutive dithers had a minimum difference.However, the approach in this paper does not necessarily produce alow-discrepancy sequence since it operates by adding small random shiftsto fixed repetitive delays.

As is well known, random sequences are often used as source ditheringtimes for allowing a better deblending. However, when multiple sourcesare used, each using such a random sequence, during the processing ofthe recoded seismic data, the dithering from one source leaks into thedithering of another source, thus making the leaked dithering sequenceto exhibit regions of clustering, which is not desirable.

A dithering sequence, when only one source is used, may be constructedto be not only random, but also to have a low-discrepancy, which avoidsthe clustering of the random sequences. A two-step algorithm 700 toachieves such good low-discrepancy sequence is illustrated as apseudo-code in FIG. 7. The algorithm 700 starts with step A forproducing a random number sequence S having Npoints=200 elements in therange [0, 1]. A function f 702 is selected for calculating a minimumdistance between a new point c 704 that is generated in the sequence Sand the previous N numbers 706 of the sequence. For this reason,function f has N different values, one for each of the previous N randomnumbers. After the sequence S is initiated with zero values in step 708and having a double number of entries than the desired Npoints, a newnumber c is generated (step 704) and compared in step 710 to theprevious N (5 in this example) numbers of the sequence based on functionf. If the result indicates that the new number c is sufficiently faraway from the previous N numbers, the new candidate c is accepted as thenext number of the sequence S. If not, the candidate c is dropped and anew candidate is generated. The candidate may be generated using arandom function in a known computer software environment.

After generating twice the necessary number of elements Npoints for thesequence, the process advances then to step B for reducing the number ofelements in the sequence S. In this regard, remember that the sequence Shas been generated in step 708 with more elements than necessary. Instep 720, only those elements of the sequence that are larger than afirst threshold (0.2 in this example) and smaller than a secondthreshold (0.8 in this example) are kept. All the other elements areremoved, and the sequence is re-scaled back to the 0-1 range. This is sobecause the values closer to the edges of the selected interval [0,1]have a tendency to cluster. To bring the elements in the sequence S tothe desired number Npoints, in step 722 only the first Npoints are kept

In numerical experiments, see, for example, Diarra 2016, it was shownthat such a low-discrepancy sequence typically improves the normalizedroot mean square (NRMS) (of deblended vs. unblended) stacks with a fewpercent compared to using a pure random sequence.

In the algorithm discussed above with regard to FIG. 7, each candidaterandom number was compared with the N last accepted numbers, and it wasrequired that it has a minimum absolute difference from each of thesenumbers. This minimum absolute difference was achieved using the ffunction. The weights given by the f function, and the number N ofprevious values to check may vary. After discarding in step B the valuesnear the minimum and maximum dither times, where they tend to cluster,the resulting sequence is a uniform random low-discrepancy sequence.

However, when applying the uniform random low-discrepancy sequence toeach source in a multi-source seismic acquisition system may not alwaysbe what is needed to achieve good deblending. In this regard, as anexample, consider the acquisition system 800 illustrated in FIG. 8A. Thesystem 800 includes a vessel 802 that tows three sources S1 to S3(source arrays in this case). To enable system 800 to extend theeffective recording time in processing, the firing time of each sourceis dithered with a dither in the range [0, 1] s. In practice, deblendingis achieved by first sorting the recorded seismic data to a commonchannel and then aligning, sequentially, the recorded seismic data forthe firing time of shot S1, S2 and S3 respectively. Notice in FIG. 8Bthat when the seismic data is aligned for source S1, the effectivedither S2-S1 and S3-S1 for sources S2 and S3 will be distributed over arange [0-2] s. This is equivalent to considering that the dither of thealigned source (S1 in this example) leaks into the dithering time of theother sources (S2 and S3 in this case).

This dither leaking has a negative impact on the seismic datacorresponding to the sources that are not aligned as now discussed. FIG.9A shows a uniform random low-discrepancy distribution for the source S1(of FIG. 8B) and FIG. 9B shows a uniform random low-discrepancydistribution for the source S2 (of FIG. 8B). Because the alignment inFIG. 8B is for the data corresponding to source S1, this effectivelymeans that the S1 dithers are added or subtracted to sources S2 and S3.If only sources S1 and S2 are considered, the resulting effectivedistribution for source S2 will be a so called Irwin-Hall distribution,as illustrated in FIG. 9C. A similar distribution is obtained when thedata for S2 or S3 is aligned. The concept is the same to adding thefaces from two dices. In this case, it is more likely to get 5, 6 or 7compared to getting 2 or 12. Adding even more dices (N→infinity), thesummed distribution will be Gaussian. This is undesired because the dataclusters as illustrated in FIGS. 9C and 9D. In other words, although thedistribution for each individual source may be constructed to be auniform random low-discrepancy sequence, due to the dither leaking, thecombination of two uniform random low-discrepancy sequences does notresult in another uniform random low-discrepancy sequence.

A non-uniform and high-discrepancy (Irwin-Hall) distribution asillustrated in FIGS. 9C and 9D is not ideal for deblending. To achievethe best possible deblending results, it is desired that the effectivedither times (S1(i)+S2(i), S2(i)+S3(i) and S3(i)+S1(i+1)) to be (1)uniform random and (2) low-discrepancy. Here T denotes the shotnumbering, where i belongs to interval [1, number of shots]. Forexample, ‘i=1’ denotes the first firing of S1, S2 and S3, while i=ndenotes the n'th firing.

To solve this problem, two conditions need to be achieved. First, it isdesired that each of sources S1, S2 and S3 follow a distribution so thatthe effective dither S1(i)−S2(i), S2(i)−S3(i) and S3(i)−S1(i+1) becomesuniform random. Second, it is desired to apply an anti-clusteringcondition to make sure that the effective dithering sequences also arelow-discrepancy.

These conditions are now implemented in numerical terms as discussednext. In analytical mathematics, no closed form solution exists to makepairs of sequences that when combined, result in a uniform randomlow-discrepancy sequence. A proof of this fact can be found, forexample, in Grimmet and Stirzaker, 2001. However, it is possible tonumerically construct S1, S2 and S3 dithering sequences with (close to)the desired properties by still generating random numbers to be added tothe sequence for each source and at the same time requiring thelow-discrepancy condition (anti-clustering) to be applied to theeffective dithers (S1(i)−S2(i), S2(i)−S3(i) and S3(i)−S1(i+1)).

The basic algorithm to achieve these sequences is illustrated in FIG.10A and includes a step 1 of selecting the number of source N (as givenby the survey layout; N is typically between 2 and 10), a step 2 ofselecting the number of dithering values nPoints, a step 3 of selectingthe number of backwards steps to use for imposing the anti-clusteringcondition (e.g., 2 to 10 backward steps may be used), a step 4 ofcreating an array of dithering values source_d(N, nPoints) to hold thedithers, and a step 5 of generating more dithers. Step 5 is repeateduntil the number of generated dithers reaches nPoints. Step 5 includes asub-step of generating M (or a number of) candidate dithers (e.g., usinguniform random numbers), a sub-step of checking whether each of thesenumbers fulfill the anti-clustering condition of the effective dithers,and a sub-step of accepting those candidates that fulfill theanti-clustering condition into the dithering value array d(N, nPoints).In step 6, the method verifies whether the number of generated dithersreaches number N. If the answers is no, the method returns to step 5. Ifthe answer is yes, the method stops in step 7.

A full pseudo-code (MatLab) 1000 is shown in FIG. 10B and achieves thesegoals as now discussed. Although the pseudo-code 1000 shows how toobtain the sequences for only three sources S1-S3, one skilled in theart would easily understand how to extend the pseudo-code to any numberof sources. In block 1002, the number of points nPoints for eachsequence is selected, and the number of backwards nBackstep values to bechecked is also selected.

In block 1004, the f-function that controls the anti-clustering is setup. In this example, the f-function is set up to be gradually reducedwithin each iteration of the while-loop in order to ensure that asolution is found within a reasonable computational time. However, inone embodiment, it is possible that the f-function is constant, i.e.,its values do not change with the shot number “i.” In block 1006, adithering value array source_d that would hold the dithering sequencesof the sources is generated and initialized. Note that no_src in thisarray represents the number of sources. In step 1008, various countersare initialized.

In block 1010, the elements (or weights) of the f-function are scaleddown to ensure that a solution is found and in block 1012 a randomnumber for each source sequence is generated. For this particular case,block 1012 generates three random numbers, one for each of the threesources S1 to S3. In block 1014, each random number generated in block1012 is checked to satisfy the anti-clustering condition for the casewhen the dithering of one source leaks into the dithering of anothersource. In this particular example, if the seismic data is aligned forthe first source S1, the anti-clustering condition is that the absolutevalue of the difference between the random number for source S1(i) andthe random number for the source S2(i) (generated in block 1012), issmaller than a corresponding value of the f-function. A similaranti-clustering condition is used for the second source S2(i). However,a slightly different anti-clustering condition is used for the third(last) source S3(i). For this case, the anti-clustering condition ischecked against the next shot S1(i+1) (see the last part of block 1014).By satisfying all these three conditions at the same time, the methodensures that when the dithering from one source leaks into the ditheringof another source, the distribution for the combined sources is close touniform random and low-discrepancy. If a solution is found in block1016, which satisfies the anti-clustering condition, the random numbersgenerated in block 1012 are added to the source_d sequence (see block1016).

In block 1018, the random numbers that are in excess of the requirednPoints are discarded. The above discussed algorithm produces dithertimes in the [0, 1] range. It is straight forward to scale this range towhatever dithering range a particular survey would require. Thus, thegenerated sequences source_d for the three sources S1 to S3, whencombined in pairs, would generate a discrete dithering sequence that isuniform random and low-discrepancy.

The three dithering sequences built for sources S1 to S3 based on themethods of FIGS. 10A and 10B are shown in FIG. 11A and theirdistributions are illustrated in FIG. 11B. It is noted in FIG. 11A thatthe dither times cluster around 0 and 1. The effective dithers(S1(i)+S2(i), S2(i)+S3(i) and S3(i)+S1(i+1)) are shown in FIG. 12A andtheir histograms are shown in FIG. 12B. These figures show theanti-clustering (low-discrepancy) and uniform distributions.

With regard to the method discussed in FIG. 10B, the step of choosingthe correct amount of anti-clustering should be carefully considered.The anti-clustering is controlled by scalars in the f array and thenumber of backwards steps (nBacksteps) variable in the pseudo-code,which makes sure that any new accepted value is sufficiently differentfrom the nBasksteps previous values. In this particular case, an f arraywith a length of 7 and coefficients from [˜0.3 . . . −0.1] was used(checking the minimum distance to the 7 previously chosen numbers). Inone embodiment, suitable coefficient values for the f array may be foundby trial and error. However, many possible solutions exist whereby onecan combine a given length of f with given coefficients. The algorithmcan be extended to work for other number of sources (dual, triple,quadruple, penta, hexa, . . . , etc.).

With a triple source as an example, it is possible to extend thealgorithm to produce low discrepancy uniform random distributions forboth S1-S2, and S1-S3. This is referred to as N+1 deblending and N+2deblending, respectively. By doing so (adding extra checks in thealgorithm in FIG. 10B), it would enable the deblending of both S2 and S3from S1—potentially allowing for very long clean record lengths. Infact, this can be extended even further, N+3, N+4 and so on.

However, numerical experiments have shown that it is difficult to get aperfectly uniform distribution in these cases. Values tend to besomewhat more densely distributed in the middle of the domain, comparedto at the edges. This is illustrated in FIGS. 13A and 13B, which showboth the N+1 and the N+2 effective dithers for a typical realization. Ascan be seen in FIGS. 13A and 13B, the histograms are not perfectly flat.Never the less, they are what it is referred to as being close touniform random, while maintaining a nice low discrepancy appearance.

The method discussed in FIG. 10B with regard to the Matlab pseudo-codeis now summarized as a flowchart in FIGS. 14A and 14B. This methodgenerates dithering sequences DS_(i) for marine seismic sources S_(i) ina marine acquisition system. The method includes a step 1400 ofdetermining a number N of the seismic sources S_(i). The number ofseismic sources may be received, for example, from the operator of theseismic survey. In step 1402, the method calculates a dithering sequenceDS_(i) for each source S_(i) such that when any two consecutive sourcesS_(k) and S_(l) are selected (where k=l+1), a combination DS_(kl) oftheir dithering sequences DS_(k) and DS_(l) is close to uniform randomlow-discrepancy sequence. The term “uniform random” means that eachelement of the dithering sequence DS_(kl) is randomly generated with astatistically speaking uniform distribution, and the term“low-discrepancy” means that an anti-clustering condition is applied toeach element of each dithering sequence DS_(kl). The method furtherincludes a step 1404 of driving each source S_(i) with the correspondingdithering sequence DS_(i) to generate blended seismic data.

The step 1402 of calculating the dithering sequence DS_(i) isschematically illustrated in FIG. 14B and includes a sub-step 1402-1 ofselecting an f-array including plural weights/coefficients to be appliedfor the anti-clustering condition to ensure that consecutive dithers aresufficiently different, avoiding any clustering. The weights (f-array)are also gradually scaled down to ensure that a solution is found ineach iteration of the algorithm within a reasonable computational time.In this particular case, the scaling is done with an exponential decay.It is of course possible to also do the scaling in other ways, or todrop this step entirely. Step 1402 further includes a sub-step 1402-2 ofselecting a number of points nPoints for each sequence DS_(i); and asub-step 1402-3 of selecting a number of backward values nBacksteps tobe used for the anti-clustering condition. A sub-step 1402-4 ofselecting a range in seconds for the elements of the sequence DS_(i) isoptional.

Step 1402 further includes a sub-step 1402-5 of generating a newcandidate dither(s) Ri, for each sequence DS_(i); and a sub-step 1402-6of verifying that the new candidate dither(s), for each sequence,satisfies the anti-clustering condition. The anti-clustering conditionverifies, for each candidate dither number R, and for each pair ofseismic sources S_(k) and S_(l), that a relation between the candidatedithers R_(k) and R_(l) is larger than a corresponding weight of thef-array.

Step 1402 further includes sub-step 1402-7 of discarding any extradithering times that were generated. Optionally, step 1402-8 scales thedithering times S_(i) to fit inside the range in seconds for theelements of the sequence DS_(i).

The above discussed method may be used in step 600 of the methodillustrated in FIG. 6B. This method has been applied to varioussynthetic and real examples and an improvement in the deblending hasbeen observed. As the synthetic example is simpler to appreciate thanthe real example, only the synthetic example is discussed herein. Asynthetic CMP-gather was generated to have 50 traces, and one flatreflector was produced (see FIG. 15A) by a 50 Hz Richer wavelet. Theblended data has been simulated by applying to the flat event in FIG.15A a ±100 ms dithered signal at twice the amplitude with a traditionaluniform random distribution for each source. This example simulatesacquired seismic data with traditional random sequences for each source,which results in an Irwin-Hall overall dither as shown in FIG. 15B. Inaddition, the blended data has been simulated with dither sequencesbased on the method of FIG. 10B. This example simulates acquired seismicdata with uniform random low-discrepancy combined sequences as shown inFIG. 15C.

Two different experiments were run on the datasets of FIGS. 15B and 15C.The first experiment just stacked up the data, and looked at the RMS andNRMS of the resulting trace compared to the unblended data. The averageresults from several thousand trials showed that the RMS values werereduced by about 1% when the uniform random low-discrepancy dither wasused compared to the Irwin-Hall dither. Interestingly, the NRMS results(comparing blended with unblended stack) showed no significantdifference.

In the second experiment, a prediction error filter (filter designed toattenuate random noise) was applied to the blended data before it wasstacked. This was to simulate a deblending process. After deblending,the RMS values of the stacks were almost exactly the same. However, itwas found a clear improvement (13%) in the NRMS when the low-discrepancyuniform random sequence was used compared to the Irwin-Hall sequence.The reason for this improvement is most likely that the uniform randomlow-discrepancy dither is more ‘random’ than an Irwin-Hall sequence. Theprediction error filter therefore does a better job in attenuating noisewith this type of dither. The results of these experiments aresummarized in FIG. 16.

The above embodiments have shown how to numerically construct a close tooptimal dither sequence for use in multisource blended acquisitionscenarios where the effective record length is extended. Experimentsshow that compared to just pure random dithering, the proposed noveldithering sequence provides a significant NRMS uplift at no additionalcost. This kind of uplift may be very important in, for example, a 4Dsetting, where one tries to detect a weak signal masked by backgroundnoise.

The above-discussed methods may be implemented in a computing device asillustrated in FIG. 17. Hardware, firmware, software or a combinationthereof may be used to perform the various steps and operationsdescribed herein.

Exemplary computing device 1700 suitable for performing the activitiesdescribed in the above embodiments may include a server 1701. Such aserver 1701 may include a central processor (CPU) 1702 coupled to arandom access memory (RAM) 1704 and to a read-only memory (ROM) 1706.ROM 1706 may also be other types of storage media to store programs,such as programmable ROM (PROM), erasable PROM (EPROM), etc. Processor1702 may communicate with other internal and external components throughinput/output (I/O) circuitry 1708 and bussing 1710 to provide controlsignals and the like. Processor 1702 carries out a variety of functionsas are known in the art, as dictated by software and/or firmwareinstructions.

Server 1701 may also include one or more data storage devices, includinghard drives 1712, CD-ROM drives 1714 and other hardware capable ofreading and/or storing information, such as DVD, etc. In one embodiment,software for carrying out the above-discussed steps may be stored anddistributed on a CD-ROM or DVD 1716, a removable media 1718 or otherform of media capable of portably storing information. These storagemedia may be inserted into, and read by, devices such as CD-ROM drive1714, disk drive 1712, etc. Server 1701 may be coupled to a display1720, which may be any type of known display or presentation screen,such as LCD, plasma display, cathode ray tube (CRT), etc. A user inputinterface 1722 is provided, including one or more user interfacemechanisms such as a mouse, keyboard, microphone, touchpad, touchscreen, voice-recognition system, etc.

Server 1701 may be coupled to other systems, such as a navigationsystem, GPS, and/or streamers. The server may be part of a largernetwork configuration as in a global area network (GAN) such as theInternet 1728, which allows ultimate connection to various landlineand/or mobile computing devices.

The disclosed exemplary embodiments provide a system and a method forgenerating one or more dithering sequences having all odd or evenmembers equal to zero and all other members having a value that islarger than a preset minimum value, which allows the deblending methodsto effectively deblend the recorded seismic data. It should beunderstood that this description is not intended to limit the invention.On the contrary, the exemplary embodiments are intended to coveralternatives, modifications and equivalents, which are included in thespirit and scope of the invention as defined by the appended claims.Further, in the detailed description of the exemplary embodiments,numerous specific details are set forth in order to provide acomprehensive understanding of the claimed invention. However, oneskilled in the art would understand that various embodiments may bepracticed without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone without the other features andelements of the embodiments or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

REFERENCES

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What is claimed is:
 1. A method for shooting plural seismic sources Siin a marine acquisition system with a deblending-designed ditheringsequence DS_(new), the method comprising: generating thedeblending-designed dithering sequence DS_(new) to include randomdithering times D_(i), a range of the dithering times D_(i) being largerthan a preset, non-zero, minimum value, wherein the non-zero, minimumvalue is between 200 and 1,000 ms; selecting a shooting sequence for theplural seismic sources Si; and shooting the plural seismic sources Si byapplying the deblending-designed dithering sequence DS_(new), based onthe shooting sequence SS, wherein all odd or all even members of theshooting sequence are shot with zero dithering times.
 2. The method ofclaim 1, wherein each absolute value of the dithering times in thedeblending-designed dithering sequence DS_(new) is smaller than amaximum preset value.
 3. The method of claim 1, further comprising:dynamically increasing the preset minimum value if a vessel towing theplural seismic sources slows down.
 4. The method of claim 1, wherein thedeblending-designed dithering sequence DS_(new) is a uniform randomlow-discrepancy sequence or is obtained by making all odd or all evenmembers of a uniform random low-discrepancy sequence to be zero.
 5. Themethod of claim 4, wherein the uniform random means that any valuewithin a given interval is equally likely or close to equally likely tobe drawn.
 6. The method of claim 4, wherein the low-discrepancy isobtained by imposing an anti-clustering condition to each element of thedithering sequence DS, and low-discrepancy means that a proportion ofpoints in the sequence falling into an arbitrary set B is close toproportional to a measure of B, as would happen on average, but not forparticular samples, for a uniform sequence.
 7. The method of claim 1,wherein the step of generating the deblending-designed ditheringsequence DS_(new) comprises: determining a number N of the seismicsources S_(i) to be fired; and calculating a dithering sequence DS_(i)for each source S_(i) such that when any two consecutive sourceactivations S_(k) and S_(l), where l=k+1, are selected, a combinationDS_(kl) of their dithering sequences DS_(k) and DS_(l) is a uniformrandom low-discrepancy sequence.
 8. A method for shooting plural seismicsources Si in a marine acquisition system with a deblending-designeddithering sequence DS_(new), the method comprising: generating thedeblending-designed dithering sequence DS_(new) to include randomdithering times D_(i), wherein either all odd or all even ditheringtimes Di of the deblending-designed dithering sequence DS_(new) arenull, and the other of the all odd or all even dithering times have arange having a value larger than a preset, non-zero, minimum value,wherein the non-zero, minimum value is between 200 and 1,000 ms; andshooting the plural seismic sources Si with the deblending-designeddithering sequence DS_(new).
 9. The method of claim 8, wherein anabsolute value of each non-zero member of the deblending-designeddithering sequence DS_(new) is smaller than a maximum preset value. 10.The method of claim 8, further comprising: dynamically increasing thepreset minimum range of values if a vessel towing the plural seismicsources slows down.
 11. The method of claim 8, wherein thedeblending-designed dithering sequence DS_(new) is a uniform randomlow-discrepancy sequence.
 12. The method of claim 11, wherein theuniform random means that any value within a given interval is equallylikely or close to equally likely to be drawn.
 13. The method of claim11, wherein the low-discrepancy is obtained by imposing ananti-clustering condition to each element of the dithering sequenceDS_(new), and low-discrepancy means that a proportion of points in thesequence falling into an arbitrary set B is close to proportional to ameasure of B, as would happen on average, but not for particularsamples, for a uniform sequence.
 14. The method of claim 8, wherein thestep of generating the deblending-designed dithering sequence DS_(new)comprises: determining a number N of the seismic sources S_(i) to befired; and calculating a dithering sequence DS_(i) for each source S_(i)such that when any two source activations S_(k) and S_(l), where l=k+2,are selected, a combination DS_(kl) of their dithering sequences DS_(k)and DS_(l) is a uniform random low-discrepancy sequence.
 15. A computingdevice for driving plural seismic sources Si in a marine acquisitionsystem with a deblending-designed dithering sequence DS_(new), thecomputing device comprising: a processor configured to, generate thedeblending-designed dithering sequence DS_(new) to include randomdithering times D_(i), a range of the dithering times D_(i) being largerthan a preset, non-zero minimum value, wherein the non-zero, minimumvalue is between 200 and 1,000 ms, and select a shooting sequence forthe plural seismic sources Si; and an interface connected to theprocessor and configured to send instructions to shoot the pluralseismic sources Si with the deblending-designed dithering sequenceDS_(new), based on the shooting sequence, wherein all odd or all evenmembers of the shooting sequence are shot with zero dithering times. 16.The device of claim 15, wherein an absolute value of each member of thedeblending-designed dithering sequence DS_(new) is smaller than amaximum preset value.
 17. The device of claim 15, wherein the processoris further configured to: dynamically increase the preset minimum valueas a vessel towing the plural seismic sources slows down.
 18. The deviceof claim 15, wherein the deblending-designed dithering sequence DS_(new)is a uniform random low-discrepancy sequence.
 19. The device of claim18, wherein the uniform random means that any value within a giveninterval is equally likely or close to equally likely to be drawn andwherein the low-discrepancy is obtained by imposing an anti-clusteringcondition to each element of each dithering sequence DS_(i), andlow-discrepancy means that a proportion of points in the sequencefalling into an arbitrary set B is close to proportional to a measure ofB, as would happen on average, but not for particular samples, for auniform sequence.
 20. A non-transitory computer readable mediumincluding computer executable instructions, wherein the instructions,when executed by a processor, implement instructions for generating adeblending-designed dithering sequences DS_(new) for marine seismicsources S_(i) in a marine acquisition system, the instructionscomprising: generating the deblending-designed dithering sequenceDS_(new) to include random dithering times D_(i), a range of thedithering times D_(i) being larger than a preset minimum value, whereinthe non-zero, minimum value is between 200 and 1,000 ms; selecting ashooting sequence for the plural seismic sources Si; and shooting theplural seismic sources Si with the deblending-designed ditheringsequence DS_(new), based on the shooting sequence, wherein all odd orall even members of the shooting sequence are shot with zero ditheringtimes.